'Bordering on the demented': Communications Minister Malcolm Turnbull scotches predictions he is after the Prime Minister's job. Photo: Alex Ellinghausen

Mr Turnbull's dinner with Mr Palmer sparked fears among some in the Coalition that he was attempting to destabilise Mr Abbott's leadership, according to reports.

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"It borders on the demented to string together a dinner with Clive Palmer and my attending, as the Communications Minister, the launch by a cross-party group of friends of the ABC and say that that amounts to some kind of threat or challenge to the Prime Minister," Mr Turnbull told reporters on Monday.

"It is quite unhinged. Now, Mr Bolt is fond of attacking what he regards as the government's enemies in the media, principal amongst whom of course he numbers the ABC. I don't think you would see anything as crazy as that on the ABC.

"I just have to say to Mr Bolt, he proclaims loudly that he is a friend of the government. Well with friends like Bolt, we don't need any enemies."

The Prime Minister was pressured by Labor during question time on Monday about whether he would back his Communications Minister or Mr Bolt in the spat.

"Madam Speaker, in any dispute between a member of my frontbench and a member of the fourth estate, I'm firmly on the side of my frontbencher," Mr Abbott said.

On Monday, Mr Bolt told Fairfax Media: ''It's a great shame and quite telling that Malcolm Turnbull attacks someone he calls the government's media friend with far more vitriol than I can recall him ever attacking one of the government's media enemies.

''This fits a pattern. No doubt he [Turnbull] will expand on this in his next Q&A appearance with Tony Jones.''

"I think it's perfectly reasonable for senior members of the Coalition to talk with independent and minor party senators because ... we have a budget to get through the Parliament," he said.

Mr Abbott added that there was ''nothing wrong'' with Mr Palmer having a relationship with the Communications Minister and others.

Commenting on Mr Turnbull's speech to the Parliamentary Friends of the ABC group, Mr Bolt wrote in News Corp Australia newspapers on Monday: "This is Turnbull, on the far left of the Liberal Party, charming a constituency that hates Abbott and which would back Turnbull to replace him — even if it still wouldn't vote Liberal.

"If only Turnbull had spent half this charm fighting for Abbott's budget. Instead, some of Abbott's troops complain he's almost gone missing in action."

Mr Bolt is personally close to Mr Abbott, who famously urged him to continue as a commentator after Mr Bolt was found guilty of breaching Section 18C of the Racial Discrimination Act.